Problem: Is the discriminant of $f$ positive, zero, or negative? ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ $y$ $x$ $y=f(x)$ Choose 1 answer: Choose 1 answer: (Choice A) A Positive (Choice B) B Zero (Choice C) C Negative
Solution: The ${\text{discriminant}}$ is a part of the quadratic formula. The sign of the discriminant tells us whether there are two roots, one root, or no roots. $\dfrac{-b\pm{\sqrt{\overbrace{{b^2-4ac}}^{\text{discriminant}}}}}{2a}$ Discriminant Roots Positive Two real roots Zero One repeated real root Negative No real root In this case, the parabola never touches the $x$ -axis, so $f$ has no real number roots. Therefore, the discriminant of $f$ is negative. The discriminant of $f$ is negative.